How can I implement a simple difference equation and plot the resulting output, all using MATLAB

I have a simple case of all initial conditions to be zero. We can consider a general form as:

 a0y(n) = b0x(n) +  b1x(n-1) + b2x(n-2) + ...+ bM x(n-M)
   -a1y(n-1) - a2y(n-2) - ...- aN y(n-N)

I have to plot the output y(n) with n varying from 0 to 500.

Both y(n) and x(n) are zero for n<0.

[Ahmed ElTahan]

Here is a function I have built to calculate it with added example. https://www.mathworks.com/matlabcentral/fileexchange/56142-output-estimation-difference-equation

Answer 1

[Wayne King]

You have not said what x(n) is, is it a white noise input. Is it the Kronecker delta sequence.

If we don't know that x(n) is we certainly can't tell you what y(n) is.

If you know x(n), you can implement using filter

 B = [b0 b1 b2 b3 .... bM];
 A = [1 a1/a0 a2/a0 ... ];
 x(n) = zeros(100,1);
 x(1) = 1; % Kronecker delta input
 y = filter(B,A,x);

[upinderjeet]

Actually x(n) is uniformly distributed random signal between -1 and 1. Now please tell me how to modify the above code according to this input and also how to define this x(n) in matlab.

Answer 2

[Wayne King]

Please look at the help for rand

 x = -1+ 2*rand(100,1);
 B = [b0 b1 b2 b3 .... bM];
 A = [1 a1/a0 a2/a0 ... ];
 y = filter(B,A,x);

[upinderjeet]

dont you think it shud be -1+ 2*rand(1,500) since I want to plot for k=0 to k=500 and also it shud be a row vector of 500 elements instead of column vector.

Answer 3

[sixwwwwww]

may be you can try something like this:

N = 500;
for n = 1:N
    xValues = sum(randi(10, 1, n) .* (rand(1, n) - 1));
    yValues = sum(randi(10, 1, n - 1) .* (rand(1, n - 1) - 1));
    y(n) = xValues - yValues;
end
plot(1:N, y)

[upinderjeet]

actually I think, x = -1+ 2*rand(1,500); should just work fine for my case as it gives me a array of 500 elements(all in one row), except the fact that when I plot this x, the points are connected in the plot. I want them to be discrete points so that I can simulate my discrete system. But the plot I am getting is have all these points connected by straight linesinstead of discrete representation where the previous value is held until the next random number. Please tell me if I can achieve that.

[sixwwwwww]

you can discrete the plot the following way:

plot(x, y, '*')

Answer 4

[Mohazam Awan]

y1=zeros(1,length(n)); % Pre-allocating
for i=1:length(n)
    if(n(i)<0)
        y1(i)=0;  % $ y[n]=0 for n<0
    end
    if (n(i)>=0)
        y1(i)=y1(i-1)+x(i);
    end
end